What is 5/12 of a full rotation

Using the conversion factors, we find that 3 cubic miles is approximately equal to 1.2504543 × 10^10 cubic meters. 5 cubic feet per second is equal to 2244.156 gallons per minute. 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

1.1. One mile is equal to 1609.34 meters. Since we're dealing with cubic units, we cube the conversion factor.

1 mile = 1609.34 meters

1 mile³ = (1609.34 meters)³ = 4.168181 × 10^9 cubic meters

Therefore, 3 cubic miles is equal to 3 * 4.168181 × 10^9 cubic meters, which is approximately 1.2504543 × 10^10 cubic meters.

1.2. To convert from cubic feet per second (ft³/s) to gallons per minute (gal/min), we use the appropriate conversion factors.

Here are the conversion factors:

1 cubic foot = 7.48052 gallons

1 minute = 60 seconds

So, we set up the conversion as follows:

5 ft³/s * 7.48052 gal/ft³ * 60 s/min = 2244.156 gal/min

Therefore, 5 cubic feet per second is equal to 2244.156 gallons per minute.

1.3. To convert centimeters (cm) to nanometers per second squared (nm/sec²), we use the appropriate conversion factors. Here are the conversion factors:

1 centimeter = 10^7 nanometers

1 second = 1 second

So, we set up the conversion as follows:

9.50 cm * (10^7 nm/cm) / (1 sec)² = 9.50 * 10^7 nm/sec²

Therefore, 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.

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Answer: The expected value of V can be calculated as the sum of the products of the possible values of V and their corresponding probabilities. Let's consider the three possible scenarios:

Using the utility function, we can see that the expected value of V is:

E[V] = 0 * 0.2 + (1/2) * (0.8 * 9/10) + 10 * (0.8 * 1/10)

E[V] = 0 + 0.36 + 0.8

E[V] = 1.16

Therefore, the expected value of V is 1.16. However, since V represents the number of healthy vacation days, it must be a non-negative integer. So, the closest integer to 1.16 is 1. Therefore, the answer is c. 2.

Answer:

Step-by-step explanation:

Are the outcomes on the two cards independent? Why?

Yes. The events can occur together. No. The probability of drawing a specific second card depends on the identity of the first card.     No. The events cannot occur together. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Answer:

4

Step-by-step explanation:

If the output value is 16, then the equation we are left with is

16 = 2x + 8

(because y is the output, or the answer)

To solve, first subtract 8 from both sides.

16 - 8 = 2x + 8 - 8

We get:

8 = 2x

Then simply divide 8 by 2.

4 = x

So, x = 4

The input would be 4 since x is our input.

Hope this helps!

The value of angle e is 55⁰.

The value of angle f is 55⁰.

The value of angle e is calculated by applying the following principles of angles on a straight line.

The vertical angle between e⁰ and 100⁰ = 25⁰ ( vertically opposite angles are equal)

The value of angle e is calculated as;

e⁰ + 25⁰ + 100⁰ = 180⁰ ( sum of angles on a straight line )

e⁰ = 180⁰ - 125⁰

e⁰ = 55⁰

The missing base angle of the triangle on the same line as e is calculated as;

? + 110⁰ = 180⁰ (sum of angles on a straight line )

? = 180 - 110

? = 70⁰

The value of angle f is calculated as;

f⁰ + e⁰ + ? = 180⁰ ( sum of angles in a triangle )

f⁰ + 55⁰ + 70⁰ = 180

f⁰ = 180 - 125⁰

f⁰ = 55⁰

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Answer:

5. =8

6= x=20 ur welcome

Answer: x = 8, x = 5

Step-by-step explanation:

first problem: first, we collect like terms

3x + 3 = 2x + 11

then, we move the terms around.

3x - 2x = 11 - 3

finally, we collect those like terms and calculate.

x = 8

second problem: first, we rewrite the expression

2 x 3x + 1 = 2x + 21

then, we calculate.

6x + 1 = 2x + 21

next, we move the terms,

6x - 2x = 21 - 1

then, we collect the like terms.

4x = 20

finally, we divide both sides.

x = 5

The future value for the given annuity, rate interest and time period is $10871000.

Given that, annuity=$100,000, rate of interest=7% and time period = 30 years.

We know that, future value =Annuity×[((1+r)ⁿ-1)/r]

Here, future value = 100,000×[((1+0.07)³⁰-1)/0.07]

= 100,000×[((1.07)³⁰-1)/0.07]

= 100,000×7.61/0.07

= 100,000×108.71

= $10871000

Therefore, the future value for the given annuity, rate interest and time period is $10871000.

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"Your question is incomplete, probably the complete question/missing part is:"

You borrow $100,000 over a period of 30 years at a fixed APR of 7%. Find the future value.

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Using the distributive property, the expanded form of (−1/4)(−8x+12y) is c) 2x - 3y.

The distributive property states that when you multiply a number or a variable expression by a sum or a difference, you can distribute the multiplication over each term within the parentheses.

So, to expand the expression (−1/4)(−8x+12y), we can apply the distributive property by multiplying -1/4 to each term inside the parentheses:

(−1/4)(−8x+12y) = (−1/4) × (−8x) + (−1/4) × (12y)

= (1/4) × 8x − (1/3) × 12y

= 2x − 3y

Therefore, the expanded form of (−1/4)(−8x+12y) is 2x − 3y. Hence, the correct answer is (c) 2x-3y.

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This is the solution to the given initial value problem using the Laplace transform method.

To solve the given IVP using the Laplace transform method, we first apply the Laplace transform to the differential equation y'' - y = t - 2 with the initial conditions y(2) = 3 and y'(2) = 0.

Taking the Laplace transform of the given equation, we get:

L{y''}(s) - L{y}(s) = L{t - 2}(s)

Now, we apply the Laplace transform properties for derivatives:

s^2Y(s) - sy(2) - y'(2) - Y(s) = (1/s^2) - (2/s)

Given the initial conditions y(2) = 3 and y'(2) = 0, we can plug them into the equation:

s^2Y(s) - 3s - Y(s) = (1/s^2) - (2/s)

Now, solve for Y(s):

Y(s) = (1/s^2) - (2/s) + 3s/(s^2 + 1) + 1/(s^2 + 1)

Next, perform the inverse Laplace transform to find y(t):

y(t) = L^{-1}{Y(s)}

y(t) = t - 2 + 3(sin(t) - 2cos(t)) + cos(t)

This is the solution to the given initial value problem using the Laplace transform method.

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An equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

Given that, focus of a parabola at (-4,3) and a directrix at y = 5.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

The standard form of the equation of the parabola is (x - h)² = 4p(y - k), where

The vertex of the parabola is (h, k)

The focus is (h, k + p)

The directrix is at y = k - p  

Here, the focus of the parabola is (4, -3)

The focus is (h, k + p)

So, h = 4

Then, k + p = -3 --------(1)

It has a directrix of y = 5

The directrix of the parabola is y = k - p

∴ k - p = 5 --------(2)

Add equations (1) and (2) to find k and p, that is

(k + k) + (p - p) = (-3 + 5)

⇒ 2k + 0 = 2

⇒ 2k = 2

Divide both sides by 2

k = 1

Substitute the value of k in equation (1), we get

1 + p = -3

Subtract 1 from both sides, we get

1 - 1 + p = -3 - 1

⇒ p = -4

Substitute the values of h=4, k=1 and p=-4 in (x - h)² = 4p(y - k), that is

(x - 4)² = 4(-4)(y - 1)

⇒ (x - 4)² = -16(y - 1)

Therefore, an equation of the parabola with the given focus and directrix is (x - 4)² = -16(y - 1).

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The endpoints after the line segments have been rotated 90 degrees counterclockwise about (-6, 4 ) is x  = (-1  3)   y = (2  2).

When a line segment is rotated 90° counterclockwise about a point it is depicted as follows:

(x  y) →  (-y  x); hence

x(3  1)  → x( -1  3 )

y(2  -2) → y(2  2)

The rules indicate that for rotation in the direction of 90 degrees:

To rotate the figure 90 degrees counterclockwise around a point, each point (x, y) will rotate (y, -x).

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Answer:

domain: 2x+1 not equal to zero, then x not equal to -1/2

Set 2x+1>0

then x>-1/2

100^(3-4x)/(2x+1)<=0.01^(5x-8)/(2x+1)

100^(3-4x)<=0.01^(5x-8)

(10^2)^(3-4x)<=[10^(-2)]^(5x-8)

10^[2*(3-4x)]<=10^[(-2)*(5x-8)]

10^(6-8x)<=10^(16-10x)

6-8x<=16-10x

2x<=10

x<=5

combine x>-1/2 and x<=5

then - 1/2<x<=5

Set 2x+1<0

then x<-1/2

100^(3-4x)/(2x+1)<=0.01^(5x-8)/(2x+1)

100^(3-4x)>=0.01^(5x-8)

(10^2)^(3-4x)>=[10^(-2)]^(5x-8)

10^[2*(3-4x)]>=10^[(-2)*(5x-8)]

10^(6-8x)>=10^(16-10x)

6-8x>=16-10x

2x>=10

x>=5

combine x<-1/2 and x>=5

, then x does not exist while 2x+1<0

so answer is - 1/2<x<=5

The simplified frame of the expression \(3 \times \frac{7 {}^{2} }{3} \times \frac{8}{3} \times 7- \frac{1}{4} \) is 6511.5.

To disentangle the given expression, we got to apply the arrange of operations (PEMDAS) and streamline the terms utilizing the example and division rules.

PEMDAS stands for Enclosures, Exponents, Multiplication and Division, and Expansion and Subtraction. We ought to perform the operations in this arrange to streamline the expression.

We rearrange the type: \(7^2 = 49\)

We rearrange the division 8/3 by partitioning the numerator by the denominator: \( \frac{8}{3} = 2 \frac{2}{3} \)

We disentangle the division 7-1/4 utilizing the run the show that a negative example is comparable to the corresponding of the base raised to the positive type: 7-1/4 = 1/74.

To revamp the expression with the rearranged values:  \(3 \times 49 / (2 \frac{2}{3} \times 1/74)\)

To partition divisions, we increase by the corresponding of the second division:  \(3 \times 49 \times 74 / (2 \frac{2}{3} )\)

We have to be rearrange the blended number  \(2 \frac{2}{3} \) by increasing the total number by the denominator and including the numerator: \(2 \frac{2}{3} = \frac{8}{3} \)

We will disentangle the expression by canceling out common variables:

3 x 49 x 74 / (8/3) = 6511.5

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

the slope is 6

Step-by-step explanation:

Answer:

Equation: y = 3x + 9

Step-by-step explanation:

To find equation:

Take two coordinates:  ( 1 , 12 ) , ( 2 , 15 )

Secondly find slope: ( y2 - y1 ) / (x2 - x1 )

Using the formula:     ( 15 - 12 ) / ( 2 - 1 )

                             :          3 ............this is our slope, m

Using formula to find equation: y - y1 = m ( x - x1 )

                                                    : y - 12 = 3 ( x - 1 )

                                                    : y = 3x - 3 + 12

                                                    :  y = 3x + 9  .....our final answer.

The equation in slope intercept form is y = 3x + 9

Answer:

y=1/4x+5

Step-by-step explanation:

1/4x is your slope you get from graphing

The values of λ1, λ2, and m, which will give us the eigenvalues of A with their algebraic multiplicities.

It is not feasible to find the answer however we can tell the method to find it out.

Given that the 3×3 matrix A has only two distinct eigenvalues, and we know that the trace of A (tr(A)) is -1 and the determinant of A (det(A)) is 45, we can find the eigenvalues and their algebraic multiplicities.

The trace of a matrix is the sum of its eigenvalues, and the determinant is the product of its eigenvalues. Since A has two distinct eigenvalues, let's denote them as λ1 and λ2.

We know that tr(A) = -1, so we have:

λ1 + λ2 + λ3 = -1 ---(1)

We also know that det(A) = 45, which is the product of the eigenvalues:

λ1 * λ2 * λ3 = 45 ---(2)

Since A has only two distinct eigenvalues, let's assume that λ1 and λ2 are the distinct eigenvalues, and λ3 is repeated with algebraic multiplicity m.

From equation (2), we have:

λ1 * λ2 * λ3 = 45

Since λ3 is repeated m times, we can rewrite this equation as:

λ1 * λ2 * \((λ3^m)\) = 45

Now, let's consider equation (1). Since A has only two distinct eigenvalues, we can write it as:

λ1 + λ2 + m*λ3 = -1

We have two equations:

λ1 * λ2 *\((λ3^m)\)= 45

λ1 + λ2 + m*λ3 = -1

By solving these equations, we can find the values of λ1, λ2, and m, which will give us the eigenvalues of A with their algebraic multiplicities.

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The ways that the exercise can be expressed such that for every 6 squares there are 3 circles include:

This question is asked in Spanish on an English site so the answer will be provided in English for better learning by other students.

The ratio of squares to circles is 6:3 or simplified, 2:1. This means for every 2 squares, there is 1 circle.

You could also use a proportional statement such that the number of squares is twice the number of circles. For every 6 squares, there are 3 circles.

There is also equation form where we can say, if S is the number of squares and C is the number of circles, the relationship could be expressed as S = 2C. This means the number of squares is twice the number of circles.

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The translated question is:

How to express this exercise for every 6 squares there are 3 circles.

Answer:

Slope: y= 4/5x+21/8

The distance is 4 units up and 5 units to the right.

Step-by-step explanation:

the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

To find th positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees, and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees,

we can use the following formulas:For a positive coterminal angle, add 360 degrees repeatedly until we reach the desired range.For a negative coterminal angle, subtract 360 degrees repeatedly until we reach the desired range.

Let's start with the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees.

To find this angle, we need to add 360 degrees repeatedly until we reach a value between 500 degrees and 1000 degrees.

So, we can write:47 + 360 = 407 (not in range)

407 + 360 = 767 (not in range)

767 + 360 = 1127 (not in range)

1127 + 360 = 1487 (not in range)

1487 + 360 = 1847 (not in range)

1847 + 360 = 2207 (not in range)

2207 + 360 = 2567 (not in range)

2567 + 360 = 2927 (not in range)

2927 + 360 = 3287 (not in range)

3287 + 360 = 3647 (not in range)

3647 + 360 = 4007 (not in range)

4007 + 360 = 4367 (not in range

4367 + 360 = 4727 (not in range)

4727 + 360 = 5087 (not in range

5087 + 360 = 5447 (not in range

)5447 + 360 = 5807 (not in range)

5807 + 360 = 6167 (not in range)

6167 + 360 = 6527 (not in range)

6527 + 360 = 6887not in range)

6887 + 360 = 7247 (not in range

)7247 + 360 = 7607 (not in range)

7607 + 360 = 7967 (not in range)

7967 + 360 = 8327 (not in range)

8327 + 360 = 8687 (not in range)

8687 + 360 = 9047 (not in range)

9047 + 360 = 9407 (not in range)

9407 + 360 = 9767 (not in range

)9767 + 360 = 10127 (not in range)

10127 + 360 = 10487 (not in range)

10487 + 360 = 10847 (not in range)

10847 + 360 = 11207 (in range)

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 11207 - 10847 = 360 degrees.

To find the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees, we need to subtract 360 degrees repeatedly until we reach a value between -500 degrees and 0 degrees. So, we can write:

47 - 360 = -313 (not in range)

-313 - 360 = -673 (not in range)

-673 - 360 = -1033 (not in range)

-1033 - 360 = -1393 (not in range

-1393 - 360 = -1753 (not in range)

-1753 - 360 = -2113 (not in range)

-2113 - 360 = -2473 (not in range)

-2473 - 360 = -2833 (not in range

-2833 - 360 = -3193 (not in range

-3193 - 360 = -3553 (not in range)

-3553 - 360 = -3913 (not in range)

-3913 - 360 = -4273 (not in range)

-4273 - 360 = -4633 (not in range)

-4633 - 360 = -4993 (in range)

therefore, the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is -4993 - (-5183) = 190 degrees.

Therefore, the positive coterminal angle to 47 degrees that is between 500 degrees and 1000 degrees is 360 degrees and the negative coterminal angle to 47 degrees that is between -500 degrees and 0 degrees is 190 degrees.

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Answer:

Step-by-step explanation:

2x+38=180

2x=142

x=71

Answer:

x = 2

Step-by-step explanation:

3x – 5 = 1

    + 5  +5

3x  = 6

x = 6 ÷ 3

x = 2

Answer:

2

Step-by-step explanation:

Step 1:

3x - 5 = 1          Equation

Step 2:

3x = 6        Add 5 on both sides

Step 3:

x = 6 ÷ 3      Divide

Answer:

x = 2

Hope This Helps :)

Answer:

( x - 2) ( x + 2 ) ( x² + 4 ) - ( x² - 3 ) ( x² + 3 )

(x² – 4) (x²+4) – ( x⁴ – 9 )

(x⁴ – 16 ) – ( x⁴ – 9)

(x⁴ – 16 ) + ( – x⁴ + 9) = – 7

I hope I helped you^_^

Answer:

0

Step-by-step explanation:

because

k  c  r

10 + (-10)

10 - 10=0

Answer:

☛☚um its 0

Step-by-step explanation:

Answer:

0.2330

Step-by-step explanation:

Answer: The translation used to create the image is 2 units to the right and 2 units up.

Step-by-step explanation: To determine the translation used to create the image, you need to compare the original figure to the image on the graph. Look at the direction and distance that the figure moved. Then, describe the movement using the words "up", "down", "left", "right", and "units".

Length of line XY is 12cm

We apply the mid-segment of trapezoid theorem:

Length of line XY is 12cm

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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